Gare Montparnasse is inside Paris, so "ticket to Paris" should be the right option. The exact wording varies between machines and locations, but it is probably the first available option on the screen on machines at CDG RER station. There's usually staff standing by to help you if you have any doubt.
Do not take "ticket t+". Those are valid only for metro (...
Looks like you want to use the Azerbaijan one. To find this, I went to Rome2Rio's page on Tbilisi to Baku. This then shows the train option with Azerbaijan Railways (ADDY)
$6 - $20 USD
And links to the rail website showing movement of the trains.
However it notes that "Buy tickets at ...
Just for completeness I will mention the existance of National Express Coaches, probably the cheapest mode of transport from Heathrow to Newcastle.
A ticket would cost £30.00 per person.
The downsides are there are no direct coaches from Heathrow, you would need to travel to London Victoria Coach Station and change there, and the time it takes to travel ...
For rail enquiries in the UK use the National Rail site. As other answers have pointed out, trains to Newcastle leaves from King's Cross station. The cheapest fares are if you buy in advance for a specific departure. However, that can be risky when coming in from a long flight with risks of delay, as the tickets would be worthless of you miss the train.
Fly. It's much faster and likely cheaper.
The LNER train from Kings Cross to Newcastle is only cheaper than flying if you book seats on a specific train, which you realistically can't do if you're flying from India - if your flight is delayed or you're held up in immigration then you'll lose your tickets.
The flight takes an hour, the train will take ...
An alternative route which might be better if you have lots of luggage and small children would be to get the Railair bus from Heathrow to Reading and then get a train to Newcastle. There are direct trains and also some which involve a change on route.